Automatically balance chemical equations using the law of conservation of mass with instant verification
You can use subscripts (₂) or regular numbers (2)
1. Balance one element at a time - Start with the most complex compound
2. Leave hydrogen and oxygen for last - They're often in multiple compounds
3. Use fractions if needed - Then multiply to get whole numbers
4. Check your work - Verify each element is balanced on both sides
5. Simplify - Reduce coefficients to smallest whole numbers
Mole ratio calculations
Burning reactions
Find limiting reagent
Maximum product
1. Balance complex first
Start with most complex molecule
2. H and O last
Leave these for final balancing
3. Verify all elements
Check atoms match on both sides
Balancing chemical equations is a fundamental skill in chemistry that ensures the law of conservation of mass is obeyed. This law states that matter cannot be created or destroyed in a chemical reaction—the number of atoms of each element must be the same on both sides of the equation. A balanced equation shows the correct stoichiometric relationships between reactants and products, which is essential for quantitative calculations in chemistry.
Antoine Lavoisier established the law of conservation of mass in the late 18th century through careful experiments. In chemical reactions, atoms are rearranged but never created or destroyed. Therefore, the total mass of reactants must equal the total mass of products. This principle is the foundation of stoichiometry and requires that all chemical equations be properly balanced.
A balanced equation has the same number of atoms of each element on both the reactant side and the product side. We achieve this by placing coefficients (whole numbers) in front of chemical formulas. These coefficients represent the number of molecules or moles of each substance involved in the reaction.
Important: We can only change coefficients, never the subscripts within chemical formulas, as changing subscripts would change the identity of the substance.
Unbalanced: H₂ + O₂ → H₂O
Count atoms:
Balance oxygen: H₂ + O₂ → 2H₂O
Balance hydrogen: 2H₂ + O₂ → 2H₂O
Balanced: 2H₂ + O₂ → 2H₂O ✓
Left: H = 4, O = 2 | Right: H = 4, O = 2
Unbalanced: C₃H₈ + O₂ → CO₂ + H₂O
Balance carbon: C₃H₈ + O₂ → 3CO₂ + H₂O
Balance hydrogen: C₃H₈ + O₂ → 3CO₂ + 4H₂O
Balance oxygen: C₃H₈ + 5O₂ → 3CO₂ + 4H₂O
Balanced: C₃H₈ + 5O₂ → 3CO₂ + 4H₂O ✓
C: 3=3, H: 8=8, O: 10=10
Unbalanced: Fe + O₂ → Fe₂O₃
Balance iron: 2Fe + O₂ → Fe₂O₃
Balance oxygen using fraction: 2Fe + (3/2)O₂ → Fe₂O₃
Clear fraction (multiply by 2): 4Fe + 3O₂ → 2Fe₂O₃
Balanced: 4Fe + 3O₂ → 2Fe₂O₃ ✓
Fe: 4=4, O: 6=6
Unbalanced: N₂ + H₂ → NH₃
Balance nitrogen: N₂ + H₂ → 2NH₃
Balance hydrogen: N₂ + 3H₂ → 2NH₃
Balanced: N₂ + 3H₂ → 2NH₃ ✓
N: 2=2, H: 6=6
This reaction is the basis for industrial ammonia production.
Also called "trial and error," this is the most common method for simple equations. You systematically adjust coefficients while checking that all elements remain balanced. This method works well for equations with only a few compounds.
For complex equations, you can set up a system of algebraic equations based on the conservation of each element. Assign variables (a, b, c, d...) to each coefficient, write equations for element conservation, and solve the system.
Example: For aFe + bO₂ → cFe₂O₃
When polyatomic ions (like SO₄²⁻, NO₃⁻, or PO₄³⁻) appear unchanged on both sides, treat them as single units instead of balancing individual elements.
Example: AgNO₃ + NaCl → AgCl + NaNO₃
NO₃ appears unchanged, so balance it as a unit (already balanced 1:1)
For hydrocarbon combustion, always balance in this order:
This order minimizes the need for adjustments.
For complex redox reactions, use the half-reaction method:
It's acceptable to use fractions temporarily during balancing, but the final answer must have whole numbers.
Example: C₃H₈ + (5/2)O₂ → 3CO₂ + 4H₂O
Multiply by 2: C₃H₈ + 5O₂ → 3CO₂ + 4H₂O
Stoichiometric Calculations: Balanced equations are essential for calculating quantities in chemical reactions. The coefficients tell us the molar ratios needed to determine how much product forms from given reactants or how much reactant is needed to produce a desired amount of product.
Industrial Chemistry: In manufacturing, balanced equations are used to calculate material requirements, predict yields, and optimize processes. An unbalanced equation would lead to incorrect calculations and costly errors in production.
Environmental Science: Balanced equations help us understand and calculate pollutant formation, greenhouse gas emissions, and the effectiveness of scrubbing and catalytic conversion processes.
Understanding Reactions: The coefficients in balanced equations reveal the fundamental particle-level behavior of reactions. They show us exactly how molecules interact and transform, providing insight into reaction mechanisms and kinetics.
Balancing equations is a skill that improves with practice. Start with simple equations and gradually work up to more complex ones. Use the examples provided in this calculator to practice, and always verify your answers by counting atoms on both sides.
Remember: Every correctly balanced equation honors Lavoisier's law of conservation of mass, one of the fundamental principles of chemistry.